The value of the discriminant of the quadratic equation $x^{2}-8x+15=0$ is ...... .

State whether the quadratic equation $2 x^{2}+x-1=0$ has two distinct real roots. Justify your answer.

The hypotenuse of a garden in the shape of a right triangle is $1$ metre more than twice the shortest side. If the longer side containing the right angle is $7$ metres more than the shorter side,find the sides of the garden.

Examine whether the following equation is quadratic or not: $\frac{x-2}{x+2} - \frac{x+2}{x-2} = \frac{3}{7}$

Verify whether the given value of $x$ is a solution of the quadratic equation or not: $6x^{2} - x - 2 = 0; x = \frac{2}{3}$

If the following quadratic equation has two equal and real roots,then find the value of $k$: $k x^{2} - 24 x + 16 = 0$.